One motivation which prompted the spike in desertions was the belief that the capture of the State capital was the handwriting on the wall that the Cause was doomed. It's understandable when you consider that the fall of Little Rock was the culmination of a series of stinging Confederate defeats at Gettysburg, Vicksburg and Helena, only two months earlier. After that triple-whammy, the fall of Little Rock was the final straw for many of the conscripts.
A second factor was the miserable state of morale among the troops. Most of the conscripts had never been paid, and many hadn't had a square meal in months. But overhanging all other complaints was the utter contempt in which they held their commanders. This appears to have been a direct result of the botched attack on Helena, two months earlier. The attack was poorly planned and executed. Many of the regiments performed magnificently, in spite of the uninspired leadership of their commanders. The charges matched any assault in the war in terms of fury and sheer bravery. Some regiments attacked and took their objectives, but their commanders fed them into the fight in an uncoordinated, piecemeal manner, so the lead regiments found themselves far ahead of their support, where they were surrounded and cut to pieces. So many good men died needlessly at Helena. The soldiers were furious at the performance of their commanders. They felt that their comrades had been needlessly sacrificed. Morale plummetted. Then when, the way they saw it, Little Rock had been abandoned without much of a fight, it was the last straw. Their letters and diaries reflect their sheer disgust with "the brass". Many were so fed up with their generals that they went home and joined the Union army. Others went home with the attitude that "when you generals are ready to get serious, give me a call."
About half of those who deserted after Little Rock eventually returned to the ranks, mostly through the entreaties of their captains and lieutenants, for whom the soldiers seemed to have a great deal of respect. But the other half were gone for good, and, as I said, enough of them switched sides to form a half-dozen Union regiments.
As in other theaters of the war, the summer and fall of 1863 in Arkansas demonstrated that the Confederate soldiers were often better than the officers who led them. I'm not saying that all the generals and colonels were blundering fools who were detested by their men -- far from it! There were some brilliant and beloved leaders in the Trans-Mississippi Army, but such men were rarely in a position to influence the overall strategy of the war in the Trans-Mississippi Department.